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ISSN 1835-9728

Environmental Economics Research Hub Research Reports

Between Estimates of the Environmental Kuznets Curve

David I Stern

Research Report No. 34

July 2009

About the authors David Stern is a Hub Researcher based at the Arndt-Corden Division of Economics, Research

School of Pacific and Asian Studies, Australian National University, Canberra, ACT 0200,

AUSTRALIA.

E-mail: sterndavidi@yahoo.com, Phone: +61-2-6161-3977.

mailto:sterndavidi@yahoo.com

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Environmental Economics Research Hub Research Reports are published by The Crawford School of Economics and Government, Australian National University, Canberra 0200 Australia. These Reports present work in progress being undertaken by project teams within the Environmental Economics Research Hub (EERH). The EERH is funded by the Department of Environment and Water Heritage and the Arts under the Commonwealth Environment Research Facility. The views and interpretations expressed in these Reports are those of the author(s) and should not be attributed to any organisation associated with the EERH. Because these reports present the results of work in progress, they should not be reproduced in part or in whole without the authorisation of the EERH Director, Professor Jeff Bennett (jeff.bennett@anu.edu.au)

Crawford School of Economics and Government THE AUSTRALIAN NATIONAL UNIVERSITY

http://www.crawford.anu.edu.au

mailto:jeff.bennett@anu.edu.auhttp://www.crawford.anu.edu.au/http://www.crawford.anu.edu.au/

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TABLE OF CONTENTS

Abstract 4

1. Introduction 5

2. Econometric Theory 6

3. Methods and Data 11

4. Results 12

5. Discussion and Conclusions 16

References 17

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Abstract

A recent paper in the Journal of Environmental Economics and Management [18] points out

that time effects are not uniquely identified in reduced form models such as the

environmental Kuznets curve and proposes a solution that assumes that the time effect is

common to each pair of most similar countries. The between estimator makes no a priori

assumption about the nature of the time effects and is likely to provide consistent estimates of

long-run relationships in real world data situations. I apply several common panel data

estimators to the data set for carbon and sulfur emissions in the OECD collected by

Vollebergh et al. [18] and the global sulfur dataset compiled by Stern and Common [13]. The

between estimates of the sulfur-income elasticity are 0.732 in the OECD and 1.157 in the

global data set and the estimated carbon-income elasticity is 1.612.

Key Words: carbon, sulfur, environmental Kuznets curve, between estimator

JEL Codes: C23, Q53, Q56

Acknowledgments: I thank Elbert Dijkgraaf for providing the data used in their paper.

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1. Introduction

A recent paper in Journal of Environmental Economics and Management [18] points out that

the time effects are not identified, a priori, in reduced form models such as the environmental

Kuznets curve (EKC) and that existing EKC regression results depend on the specific

identifying assumptions implicitly imposed. Their approach is to assume that the time effects

are identical in each pair of most similar countries. In this paper, I propose to use the simpler

between estimator – a cross section regression on the mean data for each country – as an

alternative means of estimating relationships such as the EKC free from assumptions about

the time effects. I apply the between estimator and other panel data estimators to the data sets

used by Vollebergh et al. [18] and the global sulfur dataset used by Stern and Common [13].

Panel data contains two dimensions of variation – the differences between countries – the

“between variation” and the differences over time within countries – the “within variation”.

Fixed effects estimation – also known as the “within estimator” – eliminates the average

differences between countries prior to estimation. The coefficient estimates, therefore,

primarily exploit the variation within the countries.1 The between estimator first averages the

data for each country over time. Therefore, the coefficient estimates only exploit variation

across countries and not within countries. As explained in the following section, in the

absence of a variety of misspecification issues, both these and other panel estimators should

converge on identical estimates in large samples when there are no time effects (Pesaran and

Smith, 1995). But empirically the various estimators diverge due to misspecification error

and differences in the treatment of time effects.

In contrast to the time series and panel estimators that have been used to estimate the EKC to

date, the between estimator makes no specific assumptions about the time process. To

achieve identification it makes the two standard assumptions of linear regression that the

regression slope coefficients are common to all countries (and implicitly time periods) and

that there is no correlation between the regressors and the error term. Given these

assumptions, the between estimator is a consistent estimator of the long-run relationship

between the variables when the time series are stationary or stochastically trending and is

super-consistent for cointegrating series [11].

Historically, the between estimator has been shunned by researchers due to a concern that

1 Not all variation between countries is eliminated by the subtraction of country means from the data.

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omitted variables represented by the individual effects may be correlated with the included

explanatory variables. As the individual effects are absorbed into the regression residual

term, this would be expressed as a correlation between the error term and the regressors and

lead to inconsistent estimates of the regression coefficients. The random effects estimator,

which treats the individual effects as error components, suffers from the same potential bias.

The widely used Hausman test [6] tests whether there is a significant difference between the

random effects and fixed effects estimates of a model, which should both be consistent

estimators in the absence of such a correlation (assuming that there are no other econometric

issues). There is commonly found to be a difference between these estimators in the EKC

literature [13].

However, this is only one of several potential misspecifications of panel data models. Hauk

and Wacziarg [5] show that the between estimator is the best performer among potential

panel data estimators even when the orthogonality assumption is violated but measurement

error is present.

The paper is structured as follows. The second section reviews the econometric theory

concerning potential biases in panel data estimators. It concludes that, though all estimators

may suffer from biases and/or inconsistency, the between estimator is the best practical

estimator. The third section briefly reviews the methods and data used. The fourth section

presents the results and the fifth concludes.

2. Econometric Theory

a. The Issue

Differences between time series and cross-section estimates have long been discussed in the

econometric literature [2]. In recent decades this interest has been transferred to panel data. A

time series is simply a panel data set with only one individual and a cross-section a panel

with a single time period. In addition to the estimators discussed in the introduction – within

(fixed effects), random effects, and between estimates – the econometric literature reviewed

in this section also discusses the average of static or dynamic time series regressions and OLS

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as potential estimators for panel data.2 The standard EKC model for pollution emissions is

given by:

!

ln(E /P)it

=" + #1 ln(GDP /P)it + #2(ln(GDP /P))it2 + µ

i+ $

t+ %

it (1)

where E is emissions, P population, and GDP is measured in constant purchasing power

parity adjusted dollars. i indexes countries and t time periods. The error term is composed of

an individual component µ, a time component γ, and a remainder term ε. In the general case,

all three error components are considered to be random variables. The fixed effects estimator

assumes that the individual and time components are fixed intercepts. Time series models

might treat the time component as a linear deterministic trend.

Pesaran and Smith [11] point out that if the true data generating process (DGP) is static, the

explanatory variables are uncorrelated with the error term, and any parameter heterogeneity

across individuals is random and distributed independently of the regressors, all alternative

estimators – time series or the various pooled estimators - should be consistent estimators of

the coefficient means. It is the presence of dynamics and/or correlation between the

regressors and the error term that results in differences between the estimators whether the

true parameters are homogenous or heterogeneous. There is no essential difference between

time series and cross-section estimates, only differences in the likely importance and impact

of misspecification. In the following, I address the impact of each type of misspecification on

the different estimators.

b. Coefficient Heterogeneity

Pesaran and Smith [11] argue that, in the absence of omitted variables or measurement error,

the averaged time series and between estimators are consistent for large N and T, whatever

the nature of coefficient heterogeneity. A traditional cross-section estimate, however, may

suffer from a high level of bias because T = 1. In the presence of coefficient heterogeneity,

FE and RE estimators for dynamic models will be inconsistent, as forcing the coefficients to

be equal induces serial correlation in the disturbance, which results in inconsistency when

2 There are many more potential panel data estimators including random coefficients models, maximum likelihood estimates, instrumental variable estimators etc.

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there are lagged dependent variables. If the true model is static, static FE and RE should be

consistent in the absence of other misspecifications.

Pesaran and Smith analyze both stationary and non-stationary cases – static time-series

estimates are of course superconsistent when the variables are I(1) and cointegrate. But, if the

parameters vary across groups, the pooled estimates need not cointegrate. The between

estimator is also a consistent estimator of the long-run coefficients even in the absence of

cointegration, as long as the explanatory variables are strictly exogenous. They estimate a

labor demand model (cross-section dimension: 38, time-series dimension: 29) using

heterogeneous and pooled approaches. The static cointegrating time series regressions yield

an average own price elasticity of -0.30 and a variety of dynamic time series models give

elasticities up to -0.45. The between estimate is -0.523 and static pooled estimates are: OLS: -

0.53, RE: -0.42, and FE: -0.41. Dynamic pooled estimates are much larger in absolute value,

OLS: -3.28, RE: -1.83, and FE: -0.74. The bottom line is that there are no large differences

between their static estimates though BE and OLS show greater elasticities, time series

smaller elasticities, and fixed effects occupies a mid-point. The dynamic pooled estimators,

however, deviate significantly from the estimators that Pesaran and Smith argue are

consistent.

c. Misspecified Dynamics

Baltagi and Griffin [2] examined the effect of omitted dynamics in the case of stationary

panel data. If the true data generating process (DGP) for a time series is dynamic and a static

model is estimated there are omitted lagged variables. The value of the estimated coefficients

depends on the correlation between the omitted lags and the current value of the variables.

The greater the correlation, the closer the static coefficients will be to the sum of the dynamic

coefficients – i.e. the long-run effect. The less the correlation, the closer the static estimates

will be to the impact coefficients – i.e. a short-run effect. Baltagi and Griffin argued further,

that in panel data, the higher the correlation between lagged dependent variables the better

the between estimator would estimate the long-run coefficients. The performance of the

within estimator also depends on the relative amount of between and within variation in the

data as correlations between cross-sections of demeaned data are usually lower than between

cross-sections of raw data. They carry out a Monte Carlo analysis of a model with a very long

lag structure, random effects errors, and no correlation between the explanatory variables and

those errors. They fit dynamic models to the generated data (they do not fit static models).

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Estimated lag length tends to be truncated. The between estimator gets very close to the true

long-run elasticity while the within estimator provides good estimates of the short-run

elasticity and somewhat underestimates the long-run elasticity. The within estimator is also

strongly affected by changes in the dynamic structure or length of the time series, while the

between estimator is not. All this is despite the cross-section dimension being only 18 (the

time-series dimension is 14). OLS is slightly biased upwards.

Van Doel and Kiviet [17] concluded that in general “static estimators usually underestimate

the long-run effect” when the variables are stationary but are consistent under non-

stationarity if there is cointegration. Two more recent papers further examine the

performance of static estimators for stationary data. Pirotte [12] shows that even if the time

dimension is fixed but N -> ∞ the between estimator converges to the long-run coefficients of

a dynamic model. When there is little serial correlation the within estimator converges to

short-run effects. If there are no individual effects, OLS converges to the long-run when the

sum of the lag coefficients tends to unity as well as when there is less serial correlation but

large individual effects. Egger and Pfaffermayr [3] also assume an underlying stationary,

dynamic DGP. Using Monte Carlo analysis, they find that when the explanatory variables are

not serially correlated the static within estimator is downwardly biased even compared to the

short-run effects. But when the level of serial correlation is high the within estimator

converges towards the long-run effects. On the other hand, the between estimator is biased

downwards if serial correlation is high and the time dimension is small. In their simulations,

on the whole, the parameter estimates are ranked from smallest to largest FE, RE, OLS, BE

with even BE biased down from the true value.

d. Omitted Explanatory Variables

The one-way error components model assumes that the error term in a panel model is

composed of an individual effect, which varies across individuals but is constant over time

and a remainder disturbance that varies over both time and individuals [1]. If omitted

explanatory variables are correlated with the included regressors, the regressors will be

correlated with the individual effects and/or the remainder disturbance [4]. The fixed effects

estimator eliminates the individual effects prior to estimation while the between estimator

averages over the remainder disturbances of each individual. Therefore, panel OLS, random

effects, between, and cross-section estimators will be biased if the regressors are correlated

with the individual effects and the fixed effects and time series estimators will be unbiased.

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But if the correlation is instead with the remainder disturbance, the between estimator will be

consistent (though biased when the time series dimension is small) and all the other

estimators will be inconsistent.

In the case of the EKC, there may be many omitted variables but the most important is likely

to be the state of technology [14]. While a large number of EKC studies allow for a common

series of time dummies, others do not include any time effects, while others still include

linear or more complex trends.

If a linear trend is employed and the true technology trend is not deterministic and linear, a

variable has been omitted. The rate of technological change certainly varies over time and

there may well be a correlation between income and the level of technology adopted.

Therefore, there is likely to be a correlation between both the remainder error and the

regressors and between the individual effects and the regressors. A priori, there is no reason

to prefer one estimator over the other on these grounds.

e. Measurement Error

Measurement error in the explanatory variables is a further factor to be considered [9]. As is

well-known, measurement error induces a correlation between the error term and the

regressors and biases the estimates downwards if the measurement error is not correlated with

the regressors [7]. If measurement errors are non-systematic the between estimator will

average them out over time and will be consistent but biased when the time series dimension

is small, while the within estimator amplifies the noise to signal ratio by subtracting

individual means from each time series.

Hauk and Wacziarg [5] carry out a Monte Carlo analysis of an economic growth equation to

examine the effects of both measurement error and omitted variables on alternative panel

estimators. They find that the between estimator is the best performer in terms of having the

minimum bias relative to fixed effects, random effects, and some GMM estimators

commonly used in the growth literature.

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f. Conclusion

There appears to be, therefore, a consensus that the between estimator is the best estimator –

it uses a large sample of data (compared to time series estimates) and is consistent for both

stationary and non-stationary data in the face of misspecified dynamics and heterogeneous

regression coefficients. And despite the potential for correlation between the explanatory

variables and the individual effects, it appears to perform well in real world situations [5].

Cross-section estimates may, however, be significantly biased. And there is disagreement on

the properties of other estimators whose performance depends on the specific properties of

the data.

It is likely that the data used in environmental Kuznets curve studies is stochastically trending

but that given the overly simple nature of the EKC model cointegration is unlikely [10].

Measurement error regarding PPP adjusted GDP and sulfur emissions is likely to be very

significant. There is less error in the measurement of carbon emissions. Correlation between

the regressors and omitted variables is very likely but there is no a priori reason I believe to

assume that there is a more significant correlation between the country means of the

regressors and the omitted variables than there is in the variation over time of the omitted

variables and the regressors. In these circumstances the between estimator is likely to be a

reasonably good estimator of the long-run relationship between income and emissions and at

least better than other estimators.

3. Methods and Data

Equation (1) specifies the general model. I estimate this model for sulfur and carbon

emissions. I also estimate a linear version of the model (setting ) for the between

estimator. I use each of the following estimators: Between estimator, fixed effects, random

effects, first differences, and pooled OLS. All the estimates apart from OLS are carried out

using the PREGRESS procedure in RATS which computes standard errors taking clustering

of residuals into account. OLS regressions were estimated in RATS using LINREG with the

option CLUSTER. I estimated the fixed effects and random effects models with and without

time effects. For OLS and the first differences estimator I estimated the model with and

without a linear time trend.

2 0

Because the between estimator is a consistent estimator of the long-run relationship even in

the absence of cointegration, I do not carry out tests of cointegration in this paper. The

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extracted time effects are almost certainly non-stationary and, therefore, emissions will not

cointegrate with income, but we will have a good estimate of the income elasticity of

emissions.

For the quadratic models, I computed the turning point at which the elasticity of emissions

with respect to income switches from positive to negative as well as the mean and standard

deviation of the elasticity under the assumption that the coefficients are known.

Vollebergh et al. [18] raise the influence of outliers on their simple EKC estimates. For the

between estimator I re-estimated the model eliminating one country at a time to determine to

what degree the results were sensitive to influential observations. I report the distribution

obtained from this exercise.

Vollebergh et al. compiled a data set for sulfur and carbon emissions, GDP (in real 1990

international dollars), and population for 24 OECD countries for the period 1960-2000. I also

use the Stern and Common [13] sample of sulfur emissions and GDP per capita for 73

developed and developing countries for the period 1960-1990. This allows us to evaluate the

effect of restricting the sample to just OECD countries, which Stern and Common (2001)

found had a major effect on the estimates.

4. Results

Table 1 presents the results for the EKC model applied to Vollebergh et al.’s sulfur emissions

data. The R2 statistics are not comparable across different estimation methods. The turning

points are all within sample. The mean of the income elasticity indicates which of the turning

points fall in the lower half or upper half of the income distribution – positive elasticities

indicate that the majority of the observations are on the rising limb of the EKC and vice

versa. The models with time trends or time effects have somewhat higher turning points and

more positive mean elasticities. The first difference estimates with a time trend yield the

highest turning point of $19,008 1990 PPP Dollars. Fixed and random effects estimates of the

turning points are a little higher than those in [13] for the OECD from 1960-1990 and are the

lowest of the estimators. There is little difference between these two estimates especially for

the models without time effects. In the latter case the Hausman statistic is just 0.0035

(p=1.00) and in the case of time effects 0.456 (p=0.634). This result is important because it

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indicates that the regressors do not appear to be correlated with the individual effects in this

sample. Therefore, the between estimator is not likely to suffer from this bias either.

Stern and Common [13] estimated an income elasticity of 0.67 for the OECD from the first

difference estimates, which is identical to that found here for the longer period. However,

while they found that the coefficient on the time trend in the first differences regression was -

0.020 here it is -0.048.

All these EKC estimates have a much higher degree of curvature than those in [13]. As

shown by the standard deviations of the elasticities, each country’s estimated elasticity has

typically moved over an implausibly wide range of values in the period of 40 years. For the

random effects estimator with time effects the average income elasticity in the sample goes

from 1.37 in 1960 to -1.97 in 2000. These results strongly contrast with Vollebergh et al.’s

estimates [18]. Figure 4 in their paper shows that the average income effect remains positive

through the whole time period for both sulfur and carbon. The curve is somewhat convex

down suggesting a more or less constant elasticity.

The between estimator for the quadratic model, however, clearly suffers from

multicollinearity - both regression coefficients are insignificantly different from zero. The

turning point is also very imprecisely estimated, though the elasticity has a narrower range

than all but the first difference estimates. So I also estimate a linear model. The estimated

elasticity is 0.732 though it is only significantly different from zero at the 10% level. This

finding seems congruent with Vollebergh et al.’s [18] findings.

To test the effect of influential data, I estimate the linear between estimator 24 times

eliminating one country from each estimate. The lowest elasticity estimated was when

Turkey was eliminated (0.566) and the highest when Switzerland was eliminated (0.989). The

standard deviation is 0.081. Eliminating Turkey reduced the t-statistic of the elasticity to

1.05. Omitting Switzerland increased it to 2.64.

Figure 1 presents the linear between estimate together with the income part of each of the

other estimates that include time effects. The average individual and time effect has been

added to the fixed effects estimate and the first differences estimate has been given an

intercept so that the mean fitted value is equal to the mean fitted value of the other estimators.

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The first differences curve is flatter than the others and not so different from the linear

between estimator in the upper income range. Random effects, fixed effects and OLS do not

differ very substantially from each other.

Figure 4 decomposes projected emissions based on the between estimator in a similar fashion

to Vollebergh et al. [18]. The income effect is the population weighted mean of the fitted

regression model in the given year. The time effect is population weighted mean residual.

The constant term is, therefore, included in the income effect. I have not normalized the

curves – the sum of the two curves is equal to average per capita emissions. The overall

picture is similar to Vollebergh et al.’s Figure 4a.

Table 2 presents the corresponding results for carbon emissions. The turning points are

within sample for fixed and random effects and mostly out of sample for the other estimators.

The turning point for the between estimator is effectively zero and the regression suffers from

multicollinearity, so we again also estimate a linear model for the between estimator. In each

case the majority of observations are on the rising limb of the EKC as shown by the mean

elasticities. For fixed and random effects the models with time effects have slightly lower

turning points than those without. For all the other estimators the reverse is true. The highest

turning points are found for the OLS and first difference estimators with time effects

($57,505 and $51,334) and the maximum elasticity is 1.666 for the quadratic between model.

The two-way fixed effects estimate of the turning point is almost identical to that in [18].

There is again little difference between the fixed and random effect estimates indicating that

omitted variables bias is not likely to be problematic in this sample. For the one-way model

the Hausman statistic is just 0.0035 (p=1.00) and for the two-way model 0.124 (p=0.940).

The coefficients on the time trends for OLS and first differences are negative but

substantially smaller than the estimates reported above for sulfur. There is also much less

variation around the mean of the income elasticities for all of the estimators compared to the

estimates for sulfur.

The estimated elasticity for the linear between model is 1.612 which is highly significantly

different to zero (t = 6.322). It is also significantly greater than unity (t = 2.400). To test the

effect of influential data I estimate the linear between estimator 24 times in each case

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eliminating one country from the data. Eliminating Luxembourg (1.472) results in the lowest

estimate of the elasticity while the highest estimate results when Switzerland was eliminated

(1.791). The standard deviation is just 0.059.

Figure 2 presents the analysis that Figure 1 provided for sulfur emissions. The between

estimates look plausible though the OLS ones seem to fit to the data better in a naïve sense

but are close to the between estimates throughout the income range. The first differences

curve is again flattest. Random effects and fixed effects do not differ very substantially from

each other.

Figure 5 decomposes carbon emissions based on the linear between estimator. The picture

differs from Figure 4b in [18]. Those results show no net reduction in emissions due to the

time effect over the sample period, though there is a reduction from the mid 1970s on. Still,

the income effect in these results has increased carbon emissions by more than the time effect

has reduced them. Given ongoing improvements in energy efficiency and increases in the

share of energy coming from nuclear power and natural gas over this period, it is not

unreasonable to expect an important time effect for carbon, albeit a smaller one than for

sulfur.

The results for the global sulfur dataset in Table 3 show much more similar estimates of the

income elasticity across the different estimators and the standard deviation of the elasticity is

also much smaller than for OECD sulfur data in Table 1. The between estimate of the

elasticity: 1.157 is not substantially different from the two way fixed effects estimate of

1.104. Hausman statistics are 0.0317 (p = 0.968) and 0.601 (p = 0.548) for the random effects

model without and with time effects respectively. Though the estimates without time effects

or time trends are generally lower, all but the one-way fixed effects estimate yield out of

sample turning points and in all cases the mean elasticity is positive. Figure 3 presents the

fitted income effects, which are all fairly similar to each other. These estimates suggest that

the between estimate of the elasticity from OECD data of 0.732 is not such an outlier as one

might think. But the ASL data underlying Table 3 tends to systematically underestimate

sulfur emissions from developing economies. So it is not surprising to find a higher elasticity

for this data. Restricting the sample to just OECD countries gives an elasticity for the

between estimator of 0.658 (standard error = 0.351).

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Figures 6 and 7 present the residuals or time effects for twelve of the countries for the

between estimates in Table 1 and 2. Figure 6 is comparable to Figure 2 in [15]. The

differences are that the latter study controls for the input and output structure of the economy,

the sample of countries is smaller, and the time series extend from only 1971 to 2000. The

frontier of the most efficient countries is here made up of Turkey, Switzerland (neither of

which are included in [15]) and Japan. The latter country was on the frontier for most of the

period in [15]. Australia and Turkey see a rise in emissions controlling for income, with

Australia ending the period as the dirtiest country for its income level. Canada starts the

period as the dirtiest. As found in [15], the countries end the period with the Germanic

countries and Japan the cleanest and the Anglo-Saxon and Mediterranean countries the

dirtiest with the exception of France. France is found to be relatively clean here, because [15]

controls for nuclear power. It is clear that there is no particular relationship in the sample

between income and efficiency. This explains why there is no significant difference between

the random and fixed effects estimation.

Switzerland has the lowest carbon emissions for its income level for every year in the sample.

The UK starts the sample with the highest income-adjusted carbon emissions and Australia

ends it. Turkey sees rising income adjusted emissions. So here too there is no relationship

between the individual effects and income. There is also less of a clear-cut relationship

between cultural regions and the final level of income-adjusted emissions. The Anglo-Saxon

countries are in the upper half of the distribution. But so is Germany.

5. Discussion and Conclusions

Theory suggests that the between estimator is likely to perform well as an estimator of long-

run relationships unless the correlation between the individual effects and the regressors in

the panel data model outweighs other sources of estimation bias. The between estimator gave

higher estimates of the emissions elasticity with respect to income than other estimators for

the two samples of OECD data. For sulfur, however, the results shown in Figure 4 seem

reasonably similar to Vollebergh et al.’s [18] results. In contrast to most past research, I

found quite a large time effect for carbon, but it is smaller than the effect for sulfur and

increasing energy efficiency and fuel switching could explain this effect even in the absence

of strict climate policies in most countries. Regression using defactored observations finds

that the coefficients for both the level and square of log income are significantly positive [19]

and likely results in a similarly high income elasticity.

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The between estimator is very simple to implement compared to either Vollebergh et al.’s

approach [18], a structural time series approach [15, 16] or a de-factored regression [19]. The

estimated time effects in this paper presumably include both a permanent time effect and a

transitory component. Future research could decompose the time effect into transitory and

permanent components using structural time series models or non-probabilistic filters such as

the Hodrick and Prescott filter [8]. Of course, the models in this paper leave more

unexplained than they explain. I am not advocating the simple emissions-income model as an

adequate model of emissions. However, the between estimator can provide a consistent

estimate of the income-emissions elasticity and can also be applied to more sophisticated

models such as production frontiers.

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[14] D. I. Stern, The rise and fall of the environmental Kuznets curve, World Development

32(8) (2004) 1419-1439.

[15] D. I. Stern, Beyond the environmental Kuznets curve: Diffusion of sulfur-emissions-

abating technology, Journal of Environment and Development 14(1) (2005) 101-124.

[16] D. I. Stern, The effect of NAFTA on energy and environmental efficiency in Mexico,

Policy Studies Journal 35(2) (2007) 291-322.

[17] I. T. van Doel, J. F.. Kiviet, Asymptotic consequences of neglected dynamics in

individual effects models. Statistica Neerlandica 48(1) (1994) 71 – 85.

[18] H. R. J. Vollebergh, B. Melenberg, E. Dijkgraaf, Identifying reduced-form relations

with panel data: The case of pollution and income, .Journal of Environmental

Economics and Management 58 (2009) 27–42.

[19] M. Wagner, The carbon Kuznets curve: A cloudy picture emitted by bad econometrics,

Resource and Energy Economics 30 (2008) 388-408.

19

Table 1: Vollebergh et al. Sulfur Data

Constant ln(GDP/P) ln(GDP/P)2 Time Trend

R^2 (adjusted)

Turning Point Elasticity

OLS -141.208 32.977 -1.793 0.272 9809.335 -0.754

(23.165) (5.198) (0.290) (573.342) (1.567)

OLS with Time Trend -111.706 25.859 -1.371 -0.036 0.389 12417.886 0.069

(24.955) (5.673) (0.321) (0.008) (1995.649) (1.198)

First Differences 16.409 -0.888 0.021 10246.47 -0.296

(2.191) (0.118) (675.251) (0.776)

First Differences with Time Trend 14.557 -0.738 -0.048 0.078 19007.94 0.666

(2.138) (0.116) (0.006) (3006.541) (0.645)

Fixed Effects 32.939 -1.823 0.803 8351.104 -1.354

(1.044) (0.056) (111.505) (1.594)

Fixed Effects with Time Effects 28.011 -1.499 0.821 11407.293 -0.178

(1.120) (0.062) (515.918) (1.310)

Random Effects -138.418 32.976 -1.825 8372.405 -1.346 (4.832) (1.042) (0.056) (110.769) (1.595) Random Effects with Time Effects -122.461 28.754 -1.557 10213.833 -0.529

(5.069) (1.105) (0.060) (346.063) (1.361)

Between Estimates Quadratic -64.531 15.536 -0.808 0.068 14890.973 0.334

(87.752) (19.211) (1.048) (9545.615) (0.706)

Between Estimates Linear 3.037 0.732 0.086

(3.870) (0.411)

Standard errors are in parentheses. The mean value of the elasticity is given but the standard error is the regular standard deviation not the standard error of the mean.

20

Table 2: Vollebergh et al. Carbon Data

Constant ln(GDP/P) ln(GDP/P)2 Time Trend

R^2 (adjusted)

Turning Point Elasticity

OLS -59.231 13.403 -0.667 0.568 22949.923 0.853 (10.617) (2.369) (0.132) (5422.287) (0.583)

OLS with Time Trend -42.335 9.326 -0.425 -0.021 0.633 57504.708 1.326 (12.995) (3.027) (0.175) (0.008) (56622.970) (0.371)

First Differences 5.934 -0.28 0.188 39128.776 (0.852) (0.046) (9353.152) (0.245)

First Differences with Time Trend 5.732 -0.264 -0.005 0.191 51334.001 0.763 (0.856) (0.046) (0.002) (16823.577) (0.230)

Fixed Effects 13.799 -0.711 0.954 16278.272 0.421 (0.383) (0.020) (264.012) (0.621)

Fixed Effects with Time Effects 13.943 -0.727 0.956 14425.861 0.255 (0.420) (0.023) (550.354) (0.636)

Random Effects -59.095 13.806 -0.711 16297.252 0.423 (1.777) (0.382) (0.020) (264.263) (0.622) Random Effects with Time Effects -58.735 13.769 -0.711 15849.711 0.383 (1.875) (0.405) (0.022) (396.067) (0.622)

Between Estimates Quadratic 1.74 -0.411 0.11 0.611 6.442 1.666 (55.161) (12.076) (0.659) (280.378) (0.096)

Between Estimates Linear -7.497 1.612 0.628 (2.400) (0.255)

Standard errors are in parentheses. The mean value of the elasticity is given but the standard error is the regular standard deviation not the standard error of the mean.

21

Table 3: Stern and Common Sulfur Data

Constant ln(GDP/P) ln(GDP/P)2 Time Trend

R^2 (adjusted)

Turning Point Elasticity

OLS -21.555 3.006 -0.118 0.348 331125 1.092 (11.128) (2.735) (0.166) (2114102) (0.228)

OLS with Time Trend -20.69 2.749 -0.099 -0.016 0.354 938181 1.131 (11.190) (2.754) (0.167) (0.005) (8811351) (0.193)

First Differences 2.357 -0.11 0.018 43496 0.571 (0.852) (0.054) (64100) (0.213)

First Differences with Time Trend 2.305 -0.105 -0.002 0.018 53598 0.592 (0.861) (0.055) (0.006) (92130) (0.204)

Fixed Effects 4.103 -0.206 0.899 20177 0.753 (0.438) (0.027) (5270) (0.400)

Fixed Effects with Time Effects 3.709 -0.16 0.901 101165 1.104 (0.439) (0.027) (65409) (0.311)

Random Effects -24.657 4.114 -0.206 21170 0.771 (1.757) (0.434) (0.026) (5612) (0.399) Random Effects with Time Effects -24.275 3.803 -0.174 54230 0.980 (1.756) (0.433) (0.026) (25922) (0.337)

Between Estimates Quadratic -19.423 2.426 -0.079 0.361 4066974 1.136 (12.766) (3.242) (0.203) (75496413) (0.154)

Between Estimates Linear -14.451 1.157 0.368 (1.436) (0.176)

Standard errors are in parentheses. The mean value of the elasticity is given but the standard error is the regular standard deviation not the standard error of the mean.

22

Figure 1. Vollebergh et al. Sulfur Data

6

7

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ln(GDP/P)

lnSO2PBetweenOLSFEREFD

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Figure 2. Vollebergh et al. Carbon Data

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lnCO2PBetweenOLSFDFERE

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Figure 3. Stern and Common Sulfur Data

-16

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Figure 4. Income and Time Effects: Between Estimator, Vollebergh et al. Sulfur Data

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Figure 5. Income and Time Effects: Between Estimator, Vollebergh et al. Carbon Data

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Figure 6. Sulfur Time Effects

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AUSCANFRAGERITAJPNSPASWESWITURUKDUSA

28

Figure 7. Carbon Time Effects

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AUSCANFRAGERITAJPNSPASWESWITURUKDUSA

EERH34p7EERH RR 34